Abstract:
A mathematical model describing the initial stage of a capture into parametric autoresonance in nonlinear oscillating systems is considered. The resonance corresponds to solutions with unboundedly growing energy. The stability of such solutions with respect to persistent perturbations on an asymptotically large time interval is investigated. A class of admissible perturbations is described for which a capture into parametric autoresonance occurs.
\Bibitem{Sul15}
\by O.~A.~Sultanov
\paper Stability of capture into parametric autoresonance
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 1
\pages 220--230
\mathnet{http://mi.mathnet.ru/timm1159}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3379620}
\elib{https://elibrary.ru/item.asp?id=23137991}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 295
\issue , suppl. 1
\pages 156--167
\crossref{https://doi.org/10.1134/S0081543816090169}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000394441400016}
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This publication is cited in the following 8 articles:
Oskar A Sultanov, “Stability and bifurcation phenomena in asymptotically Hamiltonian systems”, Nonlinearity, 35:5 (2022), 2513
Oskar A. Sultanov, “Autoresonance in oscillating systems with combined excitation and weak dissipation”, Physica D: Nonlinear Phenomena, 417 (2021), 132835
O. A. Sultanov, “Lyapunov Functions and Asymptotics at Infinity of Solutions of Equations that are Close to Hamiltonian Equations”, J Math Sci, 258:1 (2021), 97
Oskar A. Sultanov, “Bifurcations of autoresonant modes in oscillating systems with combined excitation”, Stud Appl Math, 144:2 (2020), 213
O. Sultanov, “Capture into parametric autoresonance in the presence of noise”, Commun. Nonlinear Sci. Numer. Simul., 75 (2019), 14–21
O. A. Sultanov, “Funktsii Lyapunova i asimptotika na beskonechnosti reshenii uravnenii, blizkikh k gamiltonovym”, Differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 163, VINITI RAN, M., 2019, 96–107
O. M. Kiselev, “Asymptotic behaviour of measure for captured trajectories into parametric autoresonance”, Nonlinear Dyn., 91:3 (2018), 1977–1983
O. Sultanov, “Stability and asymptotic analysis of the autoresonant capture in oscillating systems with combined excitation”, SIAM J. Appl. Math., 78:6 (2018), 3103–3118
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